Qubit Energy Level Required to be Unevenly Separated

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metamaterial
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TL;DR
Why does a Qubit need to have energy levels be unevenly separated?
I been reading up on quantum computers and in particular ones based on quantum harmonic oscillators. In all the articles, I have come across they mention a regular, linear LC oscillator cannot be used for a Qubit because it's energy levels are evenly spaced. Therefore, they use a non-linear inductor to create a non-linear LC oscillator which will have energy levels that are unevenly spaced. Can someone explain to me why unevenly spaced energy levels are required to create a quantum system/qubit?
 
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You need two isolated levels to form a qubit. In a linear h.o., any interaction that allows you to set the qubit by making transitions between 0 and 1 will also make transitions between 1 and 2, and so on.